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Don't have my book or audio? You can download a free sample of my book and audio lectures containing Lessons 1 and 2:
Did you read my tips on how to study and learn Math 1500? If not, here is a link to those important suggestions:
These are tips for the assignments in the Distance/Online Math 1500 course, but I strongly recommend that you do this assignment as homework even if you are taking the classroom lecture section of the course. These assignments are very good (and challenging) practice.
Here is a link to the actual assignment, in case you don't have it: You need to study Lesson 2 (Limits), Lesson 3 (Continuity), Lesson 4 (The Definition of Derivative), and Lesson 5 (The Differentiation Rules) from my Intro Calculus book to prepare for this assignment.
Classic continuity question like my Lesson 3, questions 1 to 3. Make sure you use the correct piece for f(2), limit as x approaches 2-, and limit as x approaches 2+. Hint, each piece will be used once, and only once.
This uses the Intermediate Value Theorem like my Lesson 3, questions 4 and 5. First, pull everything over to the left side of the equation, and define the left hand side as your function f(x). Note that f(x) is not a polynomial because of e^x, but since
e^x is a continuous function, you can declare f(x) is continuous. Then prove f(x) has at least one zero on (0,1).
These are rather challenging infinity limits like I teach in Lesson 2.
Part (a)
Note the e^-x part of this limit is quite simple. See my section about
Graphing Exponential Functions in Lesson 9.
Part (b)
Similar to my Lesson 2, question 12. Note that the square root of x^6 is NOT x^3, it is the absolute value of x^3 or |x^3|.
Part (c)
See my Lesson 2, Practise Problem 74 for a similar example.
Look at my Lesson 2, question 15 to understand the concepts here.
- You must find all the bottom zeroes of this function, then solve the limits as x approaches those zeros to find the vertical
asymptotes.
- You must compute the limits as x approaches infinity and negative infinity to find the horizontal asymptotes. You must do both limits and they do not have to agree. Each limit looks for its own asymptote. There could be one, two, or no horizontal asymptotes.
Classic defintion of derivative question. Very similar to my Lesson 4, question 2(b).
Classic differentiation rules practice as I teach in Lesson 5.
Read my section on Velocity and Acceleration starting on page 149. Look at my Lesson 5, question 5 and Practise Problems 86 and 87.
Part (b)
The particle stops rising when its velocity
is 0. Find t where v=0.
Part (c)
The particle hits the ground when H=0. Find t when H=0. If you do it correctly, there will be two answers for t, but one of those answers will clearly be inappropriate. That is because the particle is on the ground twice, once at the start, and once at the end.
Classic tangent line application of derivatives. Like my Lesson 5, question 2 and Practice Problems 75 to 82.
Similar to my Lesson 5, question 6 and Practice Problem 88. You can use quotient rule or product rule in this problem.
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